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x86: Improve svml_s_atanhf4_core_sse4.S
Improvements are:
1. Reduce code size (-62 bytes).
2. Remove redundant move instructions.
3. Slightly improve instruction selection/scheduling where
possible.
4. Prefer registers which get short instruction encoding.
5. Reduce rodata usage (-16 bytes).
The throughput improvement is not significant as the port 0 bottleneck
is unavoidable.
Function, New Time, Old Time, New / Old
_ZGVbN4v_atanhf, 8.821, 8.903, 0.991
This commit is contained in:
Noah Goldstein
parent
65897e9916
commit
fe1915d4f6
@ -30,96 +30,80 @@
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*
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*/
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/* Offsets for data table __svml_satanh_data_internal
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*/
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#define SgnMask 0
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#define sOne 16
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#define sPoly 32
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#define iBrkValue 160
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#define iOffExpoMask 176
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#define sHalf 192
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#define sSign 208
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#define sTopMask12 224
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#define TinyRange 240
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#define sLn2 256
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/* Offsets for data table __svml_satanh_data_internal_avx512. Ordered
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by use in the function. On cold-starts this might help the
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prefetcher. Possibly a better idea is to interleave start/end so
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that the prefetcher is less likely to detect a stream and pull
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irrelivant lines into cache. */
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#define sOne 0
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#define SgnMask 16
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#define sTopMask12 32
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#define iBrkValue 48
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#define iOffExpoMask 64
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#define sPoly 80
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#define sLn2 208
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#define TinyRange 224
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#include <sysdep.h>
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#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
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.section .text.sse4, "ax", @progbits
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ENTRY(_ZGVbN4v_atanhf_sse4)
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subq $72, %rsp
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cfi_def_cfa_offset(80)
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movaps %xmm0, %xmm5
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/* Load constants including One = 1 */
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movups sOne+__svml_satanh_data_internal(%rip), %xmm4
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movups ATANHF_DATA(sOne)(%rip), %xmm4
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movaps %xmm5, %xmm3
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/* Strip off the sign, so treat X as positive until right at the end */
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movups SgnMask+__svml_satanh_data_internal(%rip), %xmm7
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movaps %xmm4, %xmm8
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andps %xmm5, %xmm7
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movups ATANHF_DATA(SgnMask)(%rip), %xmm1
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movaps %xmm4, %xmm2
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andps %xmm1, %xmm0
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movaps %xmm4, %xmm10
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movups sTopMask12+__svml_satanh_data_internal(%rip), %xmm11
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movups ATANHF_DATA(sTopMask12)(%rip), %xmm11
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movaps %xmm4, %xmm14
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movaps %xmm11, %xmm9
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/*
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* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
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* the upper part UHi being <= 12 bits long. Then we have
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* atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
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*/
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movaps %xmm7, %xmm12
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movaps %xmm0, %xmm6
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mulps %xmm5, %xmm3
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subps %xmm0, %xmm2
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addps %xmm0, %xmm6
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subps %xmm2, %xmm10
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addps %xmm5, %xmm3
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subps %xmm0, %xmm10
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andps %xmm2, %xmm9
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/*
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* Check whether |X| < 1, in which case we use the main function.
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* Otherwise set the rangemask so that the callout will get used.
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* Note that this will also use the callout for NaNs since not(NaN < 1).
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*/
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movaps %xmm7, %xmm6
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movaps %xmm7, %xmm2
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cmpnltps %xmm4, %xmm6
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cmpltps TinyRange+__svml_satanh_data_internal(%rip), %xmm2
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mulps %xmm5, %xmm3
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subps %xmm7, %xmm8
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addps %xmm7, %xmm12
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movmskps %xmm6, %edx
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subps %xmm8, %xmm10
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addps %xmm5, %xmm3
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subps %xmm7, %xmm10
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andps %xmm8, %xmm9
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rcpps %xmm9, %xmm7
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subps %xmm9, %xmm2
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andps %xmm11, %xmm7
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/*
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* Now we feed into the log1p code, using H in place of _VARG1 and
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* later incorporating L into the reduced argument.
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* compute 1+x as high, low parts
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*/
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movaps %xmm4, %xmm7
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/*
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* Now compute R = 1/(UHi+ULo) * (1 - E) and the error term E
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* The first FMR is exact (we force R to 12 bits just in case it
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* isn't already, to make absolutely sure), and since E is ~ 2^-12,
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* the rounding error in the other one is acceptable.
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*/
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rcpps %xmm9, %xmm15
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subps %xmm9, %xmm8
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andps %xmm11, %xmm15
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/*
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* Split V as well into upper 12 bits and lower part, so that we can get
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* a preliminary quotient estimate without rounding error.
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*/
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andps %xmm12, %xmm11
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mulps %xmm15, %xmm9
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addps %xmm8, %xmm10
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subps %xmm11, %xmm12
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andps %xmm6, %xmm11
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mulps %xmm7, %xmm9
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addps %xmm2, %xmm10
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subps %xmm11, %xmm6
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/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
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mulps %xmm15, %xmm11
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mulps %xmm15, %xmm10
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mulps %xmm7, %xmm11
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mulps %xmm7, %xmm10
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subps %xmm9, %xmm14
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mulps %xmm12, %xmm15
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mulps %xmm6, %xmm7
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subps %xmm10, %xmm14
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/* Compute D = E + E^2 */
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@ -127,8 +111,8 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
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movaps %xmm4, %xmm8
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mulps %xmm14, %xmm13
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/* reduction: compute r, n */
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movdqu iBrkValue+__svml_satanh_data_internal(%rip), %xmm9
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/* reduction: compute r,n */
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movdqu ATANHF_DATA(iBrkValue)(%rip), %xmm9
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addps %xmm13, %xmm14
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/*
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@ -136,168 +120,149 @@ ENTRY(_ZGVbN4v_atanhf_sse4)
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* = R * (VHi + VLo) * (1 + D)
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* = QHi + (QHi * D + QLo + QLo * D)
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*/
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movaps %xmm14, %xmm0
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mulps %xmm15, %xmm14
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mulps %xmm11, %xmm0
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addps %xmm14, %xmm15
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movdqu iOffExpoMask+__svml_satanh_data_internal(%rip), %xmm12
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movaps %xmm14, %xmm2
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mulps %xmm7, %xmm14
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mulps %xmm11, %xmm2
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addps %xmm14, %xmm7
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movdqu ATANHF_DATA(iOffExpoMask)(%rip), %xmm12
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movaps %xmm4, %xmm14
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/* Record the sign for eventual reincorporation. */
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movups sSign+__svml_satanh_data_internal(%rip), %xmm1
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addps %xmm15, %xmm0
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addps %xmm7, %xmm2
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/*
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* Now finally accumulate the high and low parts of the
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* argument to log1p, H + L, with a final compensated summation.
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*/
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movaps %xmm0, %xmm6
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andps %xmm5, %xmm1
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movaps %xmm2, %xmm6
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andnps %xmm5, %xmm1
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movaps %xmm4, %xmm7
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/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
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orps %xmm1, %xmm3
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addps %xmm11, %xmm6
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maxps %xmm6, %xmm7
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minps %xmm6, %xmm8
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subps %xmm6, %xmm11
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movaps %xmm7, %xmm10
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andps %xmm2, %xmm3
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addps %xmm8, %xmm10
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addps %xmm11, %xmm0
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addps %xmm11, %xmm2
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subps %xmm10, %xmm7
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psubd %xmm9, %xmm10
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addps %xmm7, %xmm8
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addps %xmm8, %xmm7
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pand %xmm10, %xmm12
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psrad $23, %xmm10
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cvtdq2ps %xmm10, %xmm13
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addps %xmm8, %xmm0
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addps %xmm7, %xmm2
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/* final reconstruction */
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mulps sLn2+__svml_satanh_data_internal(%rip), %xmm13
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pslld $23, %xmm10
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paddd %xmm9, %xmm12
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psubd %xmm10, %xmm14
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/* polynomial evaluation */
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subps %xmm4, %xmm12
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mulps %xmm0, %xmm14
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movups sPoly+112+__svml_satanh_data_internal(%rip), %xmm0
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addps %xmm12, %xmm14
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mulps %xmm14, %xmm0
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mulps %xmm14, %xmm2
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movups ATANHF_DATA(sPoly+0)(%rip), %xmm7
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addps %xmm12, %xmm2
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mulps %xmm2, %xmm7
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/* Finally, halve the result and reincorporate the sign */
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movups sHalf+__svml_satanh_data_internal(%rip), %xmm4
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pxor %xmm1, %xmm4
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addps sPoly+96+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+80+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+64+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+48+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+32+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+16+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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addps sPoly+__svml_satanh_data_internal(%rip), %xmm0
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mulps %xmm14, %xmm0
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mulps %xmm14, %xmm0
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addps %xmm0, %xmm14
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movaps %xmm2, %xmm0
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addps %xmm13, %xmm14
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mulps %xmm14, %xmm4
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andnps %xmm4, %xmm0
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addps ATANHF_DATA(sPoly+16)(%rip), %xmm7
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mulps %xmm2, %xmm7
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addps ATANHF_DATA(sPoly+32)(%rip), %xmm7
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mulps %xmm2, %xmm7
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addps ATANHF_DATA(sPoly+48)(%rip), %xmm7
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mulps %xmm2, %xmm7
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addps ATANHF_DATA(sPoly+64)(%rip), %xmm7
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mulps %xmm2, %xmm7
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addps ATANHF_DATA(sPoly+80)(%rip), %xmm7
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mulps %xmm2, %xmm7
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addps ATANHF_DATA(sPoly+96)(%rip), %xmm7
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mulps %xmm2, %xmm7
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movaps ATANHF_DATA(sPoly+112)(%rip), %xmm6
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addps %xmm6, %xmm7
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mulps %xmm2, %xmm7
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mulps %xmm2, %xmm7
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mulps ATANHF_DATA(sLn2)(%rip), %xmm13
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/* We can build `sHalf` with `sPoly & sOne`. */
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andps %xmm4, %xmm6
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orps %xmm1, %xmm3
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xorps %xmm6, %xmm1
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addps %xmm2, %xmm7
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addps %xmm13, %xmm7
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mulps %xmm7, %xmm1
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/* Finish check of NaNs. */
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cmpleps %xmm0, %xmm4
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movmskps %xmm4, %edx
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cmpltps ATANHF_DATA(TinyRange)(%rip), %xmm0
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andps %xmm0, %xmm3
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andnps %xmm1, %xmm0
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orps %xmm3, %xmm0
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testl %edx, %edx
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/* Go to special inputs processing branch */
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/* Go to special inputs processing branch. */
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jne L(SPECIAL_VALUES_BRANCH)
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# LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5
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# LOE rbx rbp r12 r13 r14 r15 xmm0
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/* No registers to restore on fast path. */
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ret
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/* Restore registers
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* and exit the function
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*/
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L(EXIT):
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addq $72, %rsp
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/* Cold case. edx has 1s where there was a special value that
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needs to be handled by a atanhf call. Optimize for code size
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more so than speed here. */
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L(SPECIAL_VALUES_BRANCH):
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# LOE rbx rdx rbp r12 r13 r14 r15 xmm0 xmm5
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/* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
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call entry will be 16-byte aligned. */
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subq $56, %rsp
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cfi_def_cfa_offset(64)
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movups %xmm0, 24(%rsp)
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movups %xmm5, 40(%rsp)
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/* Use rbx/rbp for callee save registers as they get short
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encoding for many instructions (as compared with r12/r13). */
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movq %rbx, (%rsp)
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cfi_offset(rbx, -64)
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movq %rbp, 8(%rsp)
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cfi_offset(rbp, -56)
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/* edx has 1s where there was a special value that needs to be handled
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by a tanhf call. */
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movl %edx, %ebx
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L(SPECIAL_VALUES_LOOP):
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# LOE rbx rbp r12 r13 r14 r15
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/* use rbp as index for special value that is saved across calls to
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tanhf. We technically don't need a callee save register here as offset
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to rsp is always [0, 12] so we can restore rsp by realigning to 64.
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Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
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in the loop. */
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xorl %ebp, %ebp
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bsfl %ebx, %ebp
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/* Scalar math fucntion call to process special input. */
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movss 40(%rsp, %rbp, 4), %xmm0
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call atanhf@PLT
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/* No good way to avoid the store-forwarding fault this will cause on
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return. `lfence` avoids the SF fault but at greater cost as it
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serialized stack/callee save restoration. */
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movss %xmm0, 24(%rsp, %rbp, 4)
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leal -1(%rbx), %eax
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andl %eax, %ebx
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jnz L(SPECIAL_VALUES_LOOP)
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# LOE r12 r13 r14 r15
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/* All results have been written to 24(%rsp). */
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movups 24(%rsp), %xmm0
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movq (%rsp), %rbx
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cfi_restore(rbx)
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movq 8(%rsp), %rbp
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cfi_restore(rbp)
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addq $56, %rsp
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cfi_def_cfa_offset(8)
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ret
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cfi_def_cfa_offset(80)
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/* Branch to process
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* special inputs
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*/
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L(SPECIAL_VALUES_BRANCH):
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movups %xmm5, 32(%rsp)
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movups %xmm0, 48(%rsp)
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# LOE rbx rbp r12 r13 r14 r15 edx
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xorl %eax, %eax
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movq %r12, 16(%rsp)
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cfi_offset(12, -64)
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movl %eax, %r12d
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movq %r13, 8(%rsp)
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cfi_offset(13, -72)
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movl %edx, %r13d
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movq %r14, (%rsp)
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cfi_offset(14, -80)
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# LOE rbx rbp r15 r12d r13d
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/* Range mask
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* bits check
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*/
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L(RANGEMASK_CHECK):
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btl %r12d, %r13d
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/* Call scalar math function */
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jc L(SCALAR_MATH_CALL)
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# LOE rbx rbp r15 r12d r13d
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/* Special inputs
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* processing loop
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*/
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L(SPECIAL_VALUES_LOOP):
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incl %r12d
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cmpl $4, %r12d
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/* Check bits in range mask */
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jl L(RANGEMASK_CHECK)
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# LOE rbx rbp r15 r12d r13d
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movq 16(%rsp), %r12
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cfi_restore(12)
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movq 8(%rsp), %r13
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cfi_restore(13)
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movq (%rsp), %r14
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cfi_restore(14)
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movups 48(%rsp), %xmm0
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/* Go to exit */
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jmp L(EXIT)
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cfi_offset(12, -64)
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cfi_offset(13, -72)
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cfi_offset(14, -80)
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# LOE rbx rbp r12 r13 r14 r15 xmm0
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/* Scalar math fucntion call
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* to process special input
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*/
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L(SCALAR_MATH_CALL):
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movl %r12d, %r14d
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movss 32(%rsp, %r14, 4), %xmm0
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call atanhf@PLT
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# LOE rbx rbp r14 r15 r12d r13d xmm0
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movss %xmm0, 48(%rsp, %r14, 4)
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/* Process special inputs in loop */
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jmp L(SPECIAL_VALUES_LOOP)
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# LOE rbx rbp r15 r12d r13d
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END(_ZGVbN4v_atanhf_sse4)
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.section .rodata, "a"
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@ -305,56 +270,51 @@ END(_ZGVbN4v_atanhf_sse4)
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#ifdef __svml_satanh_data_internal_typedef
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typedef unsigned int VUINT32;
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typedef struct {
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__declspec(align(16)) VUINT32 SgnMask[4][1];
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typedef struct{
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__declspec(align(16)) VUINT32 sOne[4][1];
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__declspec(align(16)) VUINT32 sPoly[8][4][1];
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__declspec(align(16)) VUINT32 SgnMask[4][1];
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__declspec(align(16)) VUINT32 sTopMask12[4][1];
|
||||
__declspec(align(16)) VUINT32 iBrkValue[4][1];
|
||||
__declspec(align(16)) VUINT32 iOffExpoMask[4][1];
|
||||
__declspec(align(16)) VUINT32 sHalf[4][1];
|
||||
__declspec(align(16)) VUINT32 sSign[4][1];
|
||||
__declspec(align(16)) VUINT32 sTopMask12[4][1];
|
||||
__declspec(align(16)) VUINT32 TinyRange[4][1];
|
||||
__declspec(align(16)) VUINT32 sPoly[8][4][1];
|
||||
__declspec(align(16)) VUINT32 sLn2[4][1];
|
||||
__declspec(align(16)) VUINT32 TinyRange[4][1];
|
||||
} __svml_satanh_data_internal;
|
||||
#endif
|
||||
|
||||
__svml_satanh_data_internal:
|
||||
/* SgnMask */
|
||||
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
|
||||
/* sOne = SP 1.0 */
|
||||
.align 16
|
||||
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
|
||||
/* sPoly[] = SP polynomial */
|
||||
.align 16
|
||||
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
|
||||
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
|
||||
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
|
||||
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
|
||||
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
|
||||
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
|
||||
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
|
||||
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
|
||||
/* iBrkValue = SP 2/3 */
|
||||
.align 16
|
||||
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
|
||||
/* iOffExpoMask = SP significand mask */
|
||||
.align 16
|
||||
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
|
||||
/* sHalf */
|
||||
.align 16
|
||||
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
|
||||
/* sSign */
|
||||
.align 16
|
||||
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000
|
||||
/* SgnMask */
|
||||
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
|
||||
/* sTopMask12 */
|
||||
.align 16
|
||||
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
|
||||
/* TinyRange */
|
||||
/* iBrkValue = SP 2/3 */
|
||||
.align 16
|
||||
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
|
||||
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
|
||||
/* iOffExpoMask = SP significand mask ==*/
|
||||
.align 16
|
||||
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
|
||||
|
||||
/* sPoly[] = SP polynomial */
|
||||
.align 16
|
||||
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
|
||||
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
|
||||
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
|
||||
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
|
||||
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
|
||||
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
|
||||
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
|
||||
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
|
||||
|
||||
/* sLn2 = SP ln(2) */
|
||||
.align 16
|
||||
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
|
||||
/* TinyRange */
|
||||
.align 16
|
||||
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
|
||||
.align 16
|
||||
.type __svml_satanh_data_internal, @object
|
||||
.size __svml_satanh_data_internal, .-__svml_satanh_data_internal
|
||||
|
||||
Loading…
Reference in New Issue
Block a user